The split follows reports that 22-year-old Sara Leal alleged a one-night stand with Kutcher on his sixth wedding anniversary with Moore in September.

In the weeks since, Moore, 49, and Kutcher, 33, appeared to be working on their relationship, showing up together for Yom Kippur services and were spotted building a campfire at a lake near Santa Barbara, Calif., alongside their Kabbalah instructor.

The two stars weathered a previous cheating scandal one year earlier, when Brittney Jones, 22, claimed she had sex with Kutcher in July 2010. At the time, they took a trip to Israel for what the actor described as a spiritual journey.

Those who know the couple say the union had been under strain for some time, and spending more time apart.

"Demi loves Ashton as much as she hates public humiliation," a source close to the couple told PEOPLE when Leal's allegations first surfaced. "The marriage isn't good right now."